We will start the year with a wide variety of competition style problems.
We will introduce Gaussian integers in order to decide which integers can be written as a sum of two squares.
We will wrap up the discussion of Gaussian integers and prove which integers are the sum of two squares.
We will study the limitations of polynomials as prime generating functions.
We will study recursive formulas for generating primes.
We introduce some classic algorithms and the notion of runtime.
Following the introduction to algorithms, we are able to discuss the nuances of the P vs. NP problem.
We prove the Fundamental Theorem of Algebra with a focus on graphing.
The students battle it out in a full class Kahoot competition.
We will attempt to determine when a given graph is planar, culminating in Kuratowski's Theorem.
We will explore many interesting results about graph coloring.
We will finish the study of graph coloring and introduce basic ideas in Ramsey Theory.
Continued fractions are an interesting way to represent real numbers. We will develop an algorithm for computing continued fractions and attempt to classify periodic continued fractions.